Modeling for Field-Effect Transistors

  • Ellis Cumberbatch
Part of the European Consortium for Mathematics in Industry book series (ECMI, volume 5)

Abstract

The transistor industry is vast, in its manufacturing aspect, in the wide use of its products, and in the research it generates both applied and fundamental. In universities most of this work is done in physics and electrical engineering departments and little of its mathematical requirements have been taken up by math faculty. Yet there has been extensive work on modeling, analysis and computer algorithms, and there remain many open and significant problems. In this talk I shall describe some of the modeling, give a brief introduction to the equations governing current flow in a device, review some of the analytic and numerical approaches to the solution of these equations, and refer to some specialized problems where analysis is useful.1 In so doing I hope to pique the curiosity of some of my audience into taking a longer look at the rich phenomena in this field.

Keywords

Current Flow Parameter Extraction Multiple Steady State MOSFET Model Claremont Graduate School 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Sze, S. M.: Physics of Semiconductor Devices. John Wiley - Sons, New York, Second Edition, 1981.Google Scholar
  2. [2]
    Mock, M.S.: Analysis of Mathematical Models of Semiconductor Devices. Dublin: Boole Press 1983.MATHGoogle Scholar
  3. [3]
    Selberherr, Siegfried: Analysis and Simulation of Semiconductor Devices. Springer-Verlag Wien, New York 1984.Google Scholar
  4. [4]
    Smith, R. A.: Semiconductors. Cambridge: Cambridge University Press 1978.Google Scholar
  5. [5]
    Markowich, P.A.: The Stationary Semiconductor Device Equations. Springer-Verlag, Wien-New York 1986.Google Scholar
  6. [6]
    Shockley, W.: Electrons and Holes in Semiconductors. Van Nostrand, New York 1950.Google Scholar
  7. [7]
    Van Roosbroeck, W.: Theory of flow of electrons and holes in germanium and other semiconductors. Bell System Tech. J., 20 (1950) pp. 560–607.Google Scholar
  8. [8]
    Bank, R., Jerome, J., and Rose, D.J.: Analytical and numerical aspects of semiconductor device modeling. Computing Methods in Applied Sciences and Engineering V (R. Glowinski and J. Lions, Eds.), North Holland Publishing, Amsterdam (1982), pp. 593–597.Google Scholar
  9. [9]
    Jerome, J.: Consistency of Semiconductor Modeling: an Existence/Stability Analysis for the Stationary Van Roosbroeck System. SIAM J. Appl. Math., Vol. 45, No. 4, 1985 pp. 565–590.MathSciNetMATHGoogle Scholar
  10. [10]
    Seidman, T.: Steady state solutions of diffusion reaction systems with electrostatic convection. Nonlinear Anal., 4 (1980), pp. 623–637.MathSciNetMATHCrossRefGoogle Scholar
  11. [ll]
    Bank, R., Rose, D.J., and Fichtner, W.: Numerical methods for semiconductor simulation. SIAM J. Stat. Sci. Comp., 4 (1983), pp. 416–435.MathSciNetMATHCrossRefGoogle Scholar
  12. See also: Special Issue on Numerical Simulation of VLSI Devices. IEEE Trans. Electron Devices, Vol. ED-32 (1985).Google Scholar
  13. [12]
    Gummel, H.K.: A self-consistent iterative scheme for one-dimensional steady state transistor calculations. IEEE Trans. Electron Devices, Vol. ED-11, (1964), pp. 455–465.Google Scholar
  14. [13]
    Please, C.P.: An Analysis of Semiconductor P-N Junctions. IMA Jour. Appl. Math. (1982) 28, pp. 301–318.CrossRefGoogle Scholar
  15. [14]
    Markowich, P.A., Ringhofer, C.A.: A Singularly Perturbed Boundary Value Problem Modelling a Semiconductor Device. SIAM J. Appl. Math. Vol. 44, No. 2, (1984), pp. 231–256.MathSciNetMATHGoogle Scholar
  16. [15]
    Ringhofer, C.: An Asymptotic Analysis of a Transient p-n Junction Model. SIAM J. Appl. Math., Vol. 47, No. 3, (1987), pp. 624–642.MathSciNetMATHGoogle Scholar
  17. [16]
    Cimatti, G.: On the Shape of the Region of Depletion in a P-N Junction. Bollettino U.M.I. (5) 18-B (1981), pp. 393–409.Google Scholar
  18. [17]
    Rubinstein, I.: Multiple Steady States in One-Dimensional Electrodiffusion with Local Electroneutrality. SIAM J. Appl. Math., Vol. 47, No. 5, (1987), pp. 1076–1093.MathSciNetGoogle Scholar
  19. [18]
    Pao, H.C., Sah, C.T.: Effects of Diffusion Current on Characteristics of Metal-Oxide (insulator)-Semiconductor Transistors. Solid-State Electronics, Vol. 9 (1966) pp. 927–937.CrossRefGoogle Scholar
  20. [19]
    Brews, J.: A Charge-Sheet Model of the MOSFET. Solid-State Electronics, 21, (1978) pp. 345–355.CrossRefGoogle Scholar
  21. [20]
    Ihantola, H.K., Moll, J.L.: Design Theory of a Surface Field-Effect Transistor. Solid-State Electronics, 7, (1964) pp. 423–430.CrossRefGoogle Scholar
  22. [21]
    Pierret, R.F., Shields, J.A.: Simplified Long-Channel MOSFET Theory. Solid-State Electronics, Vol. 26 (1983) pp. 143–147.CrossRefGoogle Scholar
  23. [22]
    Van De Wiele, F.: A Long-Channel MOSFET Model. Solid State Electronics, Vol. 22, (1979), pp. 991–997.CrossRefGoogle Scholar
  24. [23]
    Ward, M., Odeh, F., Cohen, D.S.: Asymptotic Methods for MOSFET Modeling. Accepted by SIAM J. Appl. Math.Google Scholar
  25. [24]
    Berger, H.H.: Models for Contacts to Planar Devices. Solid-State Electronics, Vol. 15, (1972), p. 145.CrossRefGoogle Scholar
  26. [25]
    Loh, W.M., Swirhern, S.E., Schoeyer, T.A., Swandon, K.C. Saraswat: Modeling and Measurement of Contact Resistances. IEEE Trans. Electron Devices, Vol. ED-34, No. 3, (1987), pp. 512–524.CrossRefGoogle Scholar
  27. [26]
    Cumberbatch, E., Fang, W.: Three-Dimensional Modelling for Contact Resistance of Current Flow into a Source/Drain Region. Claremont Graduate School, Math Department, Preprint. 1988.Google Scholar
  28. [27]
    Gribben, R.J., Martelli, M., Rykken, C., Meiser, V., Turner, G., Wang. Q.: Parameter Extraction and Transistor Model. Mathematics Clinic, Claremont Graduate School, Final Report, 1985.Google Scholar
  29. [28]
    Gribben, R.J., Martelli, M.: Optimal parameter extraction of the Brews charge-sheet MOSFET model. Math. Engng. hid., Vol 1, No. 2, 1987, pp. 155–168.MATHGoogle Scholar
  30. [29]
    Andersson, G., Allen, D., Fleishman, R., Hamza, H., Lacey, S., Larsson, K., Panagiotacopulos, D., Velasco-Hernandez, J.: Parameter Extraction from a Nonlinear MOSFET Model. Mathematics Clinic, Claremont Graduate School, Final Report, 1988.Google Scholar

Copyright information

© B. G. Teubner Stuttgart and Kluwer Academic Publishers 1990

Authors and Affiliations

  • Ellis Cumberbatch
    • 1
  1. 1.Mathematics DepartmentThe Claremont Graduate SchoolClaremontUSA

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